How to make rigid bodies freeze?
If you want the cube to fall to bits on the plane then the plane needs to be a 'passive' object in the rigid body world so that it interacts with other objects.

If you want the cube to shatter in all directions you can turn gravity off but will still find pieces will pass through the plane if the plane is not part of the rigid body world.

Once everything is included in the rigid body world, you will then have to adjust parameters like collision margin and solver steps/iterations to make the pieces fall naturally on the plane and not penetrate it.